1. Field of the Invention
The invention is related generally to the field of well logging instruments and measurement techniques. More specifically, the invention is related to methods for processing signals from electromagnetic well logging instruments to determine a position of the instrument with respect to a conductivity discontinuity in earth formations surrounding the instrument.
2. Description of the Related Art
Wellbores drilled through earth formations to drain fluids such as petroleum are frequently drilled along a substantially horizontal trajectory in a petroleum reservoir to increase the drainage area in the reservoir. See, for example, MWD resistivity tool guides bit horizontally in thin bed, Oil and Gas Journal Dec. 9, 1991. Because petroleum reservoirs are frequently located in layered earth formations, the position of such substantially horizontal wellbores with respect to the boundaries of the layers in the earth formations often has a material effect on the productivity of such wellbores. Estimation of distances to layer boundaries, therefore, is important for well landing and drain-hole positioning.
Techniques known in the art for estimation of the wellbore position with respect to layer boundaries include those which are indirectly based on well logging measurements in close-by (xe2x80x9coffsetxe2x80x9d) wellbores. These techniques assume that the composition and the geometry of the formation layers proximate to the wellbore of interest are substantially the same as in the offset wellbores.
Another group of prior art techniques is based on the observation of features, referred to as xe2x80x9chornsxe2x80x9d, which appear in measurements made by electromagnetic-type well logging instruments, where this type of instrument approaches a layer boundary across which is a large contrast in electrical resistivity. Qualitative estimates of the distance between the instrument and the layer boundary are made by observing the magnitude of the horns.
The techniques known in the art for determining the position of the wellbore with respect to layer boundaries generally rely on well log measurements from a nearby (xe2x80x9coffsetxe2x80x9d) well or a xe2x80x9cpilotxe2x80x9d well. A pilot well is a wellbore drilled substantially vertically through the same earth formations through which a horizontal wellbore is to be drilled. Typically, it is assumed that the layered structure observed in the offset well or pilot well extends to the geographic position of the proposed horizontal wellbore without much variation and without much change in attitude of the layer boundaries. This assumption is often inaccurate, particularly in the case of horizontal wells whose ultimate horizontal extent may be several kilometers from the position of the pilot well or offset well. Further, the prior art technique of observing horns on electromagnetic propagation measurements has several limitations. First, observation of the horns has not proven to be quantitatively accurate. Second, horns are generally observed on the well log only when the instrument is very close to the boundary.
Correction of the wellbore trajectory using horn observation techniques is often too late to avoid penetrating an undesirable layer of the earth formations, such as a water-bearing layer disposed below a hydrocarbon reservoir. The horn observation technique also depends on factors such as having a large resistivity contrast between adjacent layers of the formation, and whether the formation layer boundary is disposed at a xe2x80x9cdipxe2x80x9d angle suitable for generation of the horns in the resistivity measurements. Anisotropy in the electric conductivity and dielectric permittivity of the layers of the earth formations make the quantitative use of resistivity horns even more difficult.
Techniques known in the art for determining a wellbore trajectory using horn observation, and related techniques, are described, for example, in U.S. Pat. No. 5,241,273 issued to Luling; U.S. Pat. No. 5,495,174 issued to Tao et al; and U.S. Pat. No. 5,230,386 issued to Wu et al. Techniques known in the art for so-called xe2x80x9cinversionxe2x80x9d processing measurements from well logging instruments are described in a number of patents. See, for example, U.S. Pat. No. 6,047,240 issued to Barber et al; U.S. Pat. No. 5,345,179 issued to Habashy et al; U.S. Pat. No. 5,214,613 issued to Esmersoy; U.S. Pat. No. 5,210,691 issued to Freedman; and U.S. Pat. No. 5,703,773 issued to Tabarovsky et al.
Inversion processing techniques known in the art have as one primary purpose, among others, determining the spatial distribution of physical properties, particularly conductivity, of earth formations surrounding the well logging instrument. Inversion processing generally includes making an initial model of the spatial distribution of formation properties, calculating an expected response of the well logging instrument to the model, and comparing the expected response to the measured response of the logging instrument. If differences between the expected response and the measured response exceed a predetermine threshold, the model is adjusted and the process is repeated until the differences fall below the threshold. The model, after adjustment that results in the reduced differences, then represents a likely distribution of properties of the earth formations.
Inversion processing known in the art is primarily concerned with determining the values of the properties as well as their spatial distribution. It is typically assumed that the properties of the earth formations extend laterally away from the well logging instrument a sufficient distance so that any lateral variations in the formation properties do not materially affect the response of the logging instrument. In cases where this assumption is not true, such as where the well logging instrument axis is highly inclined with respect to various layer boundaries in the formations, improved inversion techniques account for localized instrument response anomalies near these boundaries. Generally, the inversion techniques known in the art, however, do not have as a primary purpose determining the position of the wellbore with respect to layer boundaries.
An inversion processing method described in U.K. published patent application GB 2 301 902 A filed by Meyer discloses determining a distance from a well logging instrument to a layer boundary in an earth formation. The method disclosed in the Meyer ""902 A application does not have the capability for determining distances to more than one boundary simultaneously, nor does that method have the capability to determine distances from the layer boundary to the instrument simultaneously at more than one position along the wellbore trajectory.
It is desirable to provide a technique for quantitative estimation of a distance between a well logging instrument disposed in a wellbore and a boundary between layers of earth formations through which the wellbore passes or will eventually pass that is quantitative and does not require the instrument to be very close to any layer boundaries. It is also desirable to provide a technique to quantitatively estimate distances from a well logging instrument to layer boundaries where there is more than one boundary in a layered formation, and over a selected interval or segment of the wellbore, so that the trajectory of the wellbore with respect to the layer boundaries can be more precisely determined.
The invention provides a method for determining the position of a wellbore with respect to layer boundaries in earth formations. The method includes projecting a trajectory of the wellbore onto an initial model of the earth formations, selecting a segment of the trajectory and calculating, along the segment, the expected responses of a well logging instrument. Differences between the expected responses and the responses measured by the instrument along the segment are determined. The model is adjusted, the expected responses are recalculated and the differences are again determined. These are repeated until the differences fall below a selected threshold.
In one embodiment, the attitude (xe2x80x9cdipxe2x80x9d) of the formation layers with respect to the wellbore trajectory is determined as a result of the process. The wellbore in this embodiment can be extended, using the determined dip, so as to maintain the trajectory within a selected layer of the earth formations.
One embodiment of the invention includes calculating distributions of electric and magnetic fields induced by a transmitter on the instrument at each instrument position along the trajectory segment, and calculating a corresponding receiver response at each instrument position. In this embodiment, the transmitters and receivers are approximated as magnetic dipoles.
In a particular embodiment, the inversion results at least one selected point along the trajectory are calculated to provide a Bayesian minimum uncertainty. This improves the accuracy of the inversion calculations.